Question

Which of the following is a solution to the linear-quadratic system:

y=x2+3x−13


y=5


(1 point)
Responses

(−6, 3)
(−6, 3)

(3, 5)
(3, 5)

(6, 5) and (−3, 5)
(6, 5) and (−3, 5)

(3, 5) and (-6, 5)

Answer 1

To find the solution to the linear-quadratic system given by the equations:

1. \( y = x^2 + 3x - 13 \)
2. \( y = 5 \)

We can substitute \( y = 5 \) into the first equation to find the corresponding \( x \)-values.

Substituting \( y = 5 \):

\[
5 = x^2 + 3x - 13
\]

Rearranging this gives us:

\[
x^2 + 3x - 18 = 0
\]

Next, we can factor this quadratic equation:

\[
(x + 6)(x - 3) = 0
\]

Setting each factor to zero gives us:

\[
x + 6 = 0 \quad \Rightarrow \quad x = -6
\]
\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]

The solutions for \( x \) are \( x = -6 \) and \( x = 3 \). Since \( y = 5 \), we can now write the solutions as points in the coordinate system:

1. \( (-6, 5) \)
2. \( (3, 5) \)

Now, looking at your choices, the correct response is:

**(3, 5) and (-6, 5)**